# GraphMoRE: Mitigating Topological Heterogeneity via Mixture of Riemannian Experts

arXiv: https://arxiv.org/abs/2412.11085 · HTML: https://mlsanity.com/paper/2412.11085/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2024.

## Built on by (most cited first, 24 of 24)

- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [GRAVER: Generative Graph Vocabularies for Robust Graph Foundation Models Fine-tuning](https://mlsanity.com/paper/2511.05592/) (2025)
- [MoSE: Unveiling Structural Patterns in Graphs via Mixture of Subgraph Experts](https://mlsanity.com/paper/2509.09337/) (2025)
- [Learning Graph Foundation Models on Riemannian Graph-of-Graphs](https://mlsanity.com/paper/2605.09993/) (2026)
- [The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learning](https://mlsanity.com/paper/2606.06397/) (2026)
- [Learnable Kernel Density Estimation for Graphs and Its Application to Graph-Level Anomaly Detection](https://mlsanity.com/paper/2505.21285/) (2025)
- [Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction](https://mlsanity.com/paper/2510.04522/) (2025)
- [Variational Mixture of Graph Neural Experts for Alzheimer's Disease Recognition across Frequency Bands in EEG Brain Networks](https://mlsanity.com/paper/2510.11917/) (2025)
- [Dynamic Graph Prompting via Topology-Routed Mixed-Curvature Experts](https://mlsanity.com/paper/2608.06031/) (2026)
- [Leveraging Manifold Embeddings for Enhanced Graph Transformer Representations and Learning](https://mlsanity.com/paper/2507.07335/) (2025)
- [Adaptive Riemannian Graph Neural Networks](https://mlsanity.com/paper/2508.02600/) (2025)
- [CAT: Curvature-Adaptive Transformers for Geometry-Aware Learning](https://mlsanity.com/paper/2510.01634/) (2025)
- [Topology-Aware Multiscale Mixture of Experts for Efficient Molecular Property Prediction](https://mlsanity.com/paper/2601.12637/) (2026)
- [Modality as Heterogeneity: Node Splitting and Graph Rewiring for Multimodal Graph Learning](https://mlsanity.com/paper/2602.00067/) (2026)
- [Decoupled and Divergence-Conditioned Prompt for Multi-domain Dynamic Graph Foundation Models](https://mlsanity.com/paper/2605.13540/) (2026)
- [A roadmap for curvature-based geometric data analysis and learning](https://mlsanity.com/paper/2510.22599/) (2025)
- [Self-Adaptive Graph Mixture of Models](https://mlsanity.com/paper/2511.13062/) (2025)
- [Scalable Heterogeneous Graph Learning via Heterogeneous-aware Orthogonal Prototype Experts](https://mlsanity.com/paper/2601.05537/) (2026)
- [Zero-shot Generalizable Graph Anomaly Detection with Mixture of Riemannian Experts](https://mlsanity.com/paper/2602.06859/) (2026)
- [Modality-Guided Mixture of Structured Experts with Entropy-Triggered Routing for Multimodal Recommendation](https://mlsanity.com/paper/2602.20723/) (2026)
- [SAHG: Sector-Anisotropic Hyperbolic Graph Model for Social Bot Detection](https://mlsanity.com/paper/2605.30166/) (2026)
- [mathbbSL(n) Representation Learning: An Intrinsic Mixed-Curvature Space with Higher Curvature Capacities and Deeper Order-Aware Composition](https://mlsanity.com/paper/2609.15083/) (2026)
- [Riemannian Graph Tokenizer for Structural Knowledge Transfer](https://mlsanity.com/paper/2610.15427/) (2026)

## Abstract (arXiv)

Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex geometric shapes, resulting in low-quality embeddings with high distortion. This also constitutes a critical challenge for graph foundation models, which are expected to uniformly handle a wide variety of diverse graph data. Recent studies have indicated that product manifold gains the possibility to address topological heterogeneity. However, the product manifold is still homogeneous, which is inadequate and inflexible for representing the mixed heterogeneous topology. In this paper, we propose a novel Graph Mixture of Riemannian Experts (GraphMoRE) framework to effectively tackle topological heterogeneity by personalized fine-grained topology geometry pattern preservation. Specifically, to minimize the embedding distortion, we propose a topology-aware gating mechanism to select the optimal embedding space for each node. By fusing the outputs of diverse Riemannian experts with learned gating weights, we construct personalized mixed curvature spaces for nodes, effectively embedding the graph into a heterogeneous manifold with varying curvatures at different points. Furthermore, to fairly measure pairwise distances between different embedding spaces, we present a concise and effective alignment strategy. Extensive experiments on real-world and synthetic datasets demonstrate that our method achieves superior performance with lower distortion, highlighting its potential for modeling complex graphs with topological heterogeneity, and providing a novel architectural perspective for graph foundation models.